Emily is 6 years older than Jessica. Emily and Jessica first met 3 years ago. Seven years ago, Emily was 4 times older than Jessica. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Jessica. Let Emily's current age be $e$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $e = j + 6$ Seven years ago, Emily was $e - 7$ years old, and Jessica was $j - 7$ years old. The information in the second sentence can be expressed in the following equation: $e - 7 = 4(j - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = e - 6$ . Substituting this into our second equation, we get the equation: $e - 7 = 4($ $(e - 6)$ $ -$ $ 7)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 7 = 4e - 52$ Solving for $e$ , we get: $3 e = 45$ $e = 15$.